arXiv subjects

Vladimir Batagelj

Publications and source records attributed to Vladimir Batagelj.

At least 19 recordsLinked to original sources

arXiv2025

Drilling into Erasmus learning mobility flows between countries 2014-2024

Analyzing the Erasmus mobility network, we illustrate typical problems and approaches in analyzing weighted networks. We propose alternative exploratory views on the network "Erasmus+ learning mobility flows since 2014". The network has 35 nodes (countries), is very dense, and the range of link weights (number of visits) is huge (from 1 to 217003). An increasing transformation is used to reduce the range. The traditional graph-based visualization is unreadable. To gain insight into the structure of a dense network, it can be reduced to a skeleton by removing less essential links and/or nodes. We have determined the 1-neighbors and 2-neighbors subnetworks. The 1-neighbors skeleton highlights Spain as the main attractor in the network. The 2-neighbors skeleton shows the dominant role of Spain, Germany, France, and Italy. The hubs and authorities, Pathfinder and Ps cores methods confirm these observations. Using the "right" order of the nodes in a matrix representation can reveal the network structure as block patterns in the displayed matrix. The clustering of network nodes based on corrected Salton dissimilarity again shows the dominant role of Spain, Germany, France, and Italy, but also two main clusters of the division into developed/less developed countries. The Balassa normalization (log(measured/expected) visits) matrix shows that most visits within the two main clusters are above expected, while most visits between them are below expected; within the clusters of Balkan countries, Baltic countries, {SK, CZ, HU}, {IS, DK, NO} visits are much above expected, etc.

cs.SI↗

arXiv2025

Towards a format for describing networks / 1. Networks and knowledge graphs

The relationship between the concepts of network and knowledge graph is explored. A knowledge graph can be considered a special type of network. When using a knowledge graph, various networks can be obtained from it, and network analysis procedures can be applied to them. RDF is a formalization of the knowledge graph concept for the Semantic Web, but some of its solutions are also extensible to a format for describing general networks.

cs.SI↗

arXiv2025

OpenAlex2Pajek -- an R Package for converting OpenAlex bibliographic data into Pajek networks

For analysis of bibliographic data, we can obtain from bibliographic databases the corresponding collection of bibliographic networks. Recently OpenAlex, a new open-access bibliographic database, became available. We present OpenAlex2Pajek, an R package for converting OpenAlex data into a collection of Pajek's networks. For an illustration, we created a temporal weighted network describing the co-authorship between world countries for years from 1990 to 2023. We present some analyses of this network.

cs.DL↗

arXiv2024

Weighted degrees and truncated derived bibliographic networks

Large bibliographic networks are sparse -- the average node degree is small. This is not necessarily true for their product -- in some cases, it can ``explode'' (it is not sparse, increases in time and space complexity). An approach in such cases is to reduce the complexity of the problem by limiting our attention to a selected subset of important nodes and computing with corresponding truncated networks. The nodes can be selected by different criteria. An option is to consider the most important nodes in the derived network -- nodes with the largest weighted degree. It turns out that the weighted degrees in the derived network can be computed efficiently without computing the derived network itself.

physics.soc-ph↗

arXiv2023

On weighted two-mode network projections

The standard and fractional projections are extended from binary two-mode networks to weighted two-mode networks. Some interesting properties of the extended projections are proved.

cs.SI↗

arXiv2023

Cores in multiway networks

The notion of a core is generalized to multiway networks. To determine the multiway cores, we adapted already-known algorithms for determining the generalized cores in one-mode and two-mode networks. A new node property, node diversity has been introduced. The newly introduced notions are illustrated with application on the multiway networks of European airports and airlines and Summer Olympic medals till 2016. For the interactive inspection of the results, their 3D layout in X3D is supported.

physics.soc-ph↗

arXiv2023

Exactly mergeable summaries

In the analysis of large/big data sets, aggregation (replacing values of a variable over a group by a single value) is a standard way of reducing the size (complexity) of the data. Data analysis programs provide different aggregation functions. Recently some books dealing with the theoretical and algorithmic background of traditional aggregation functions were published. A problem with traditional aggregation is that often too much information is discarded thus reducing the precision of the obtained results. A much better, preserving more information, summarization of original data can be achieved by representing aggregated data using selected types of complex data. In complex data analysis the measured values over a selected group $A$ are aggregated into a complex object $Σ(A)$ and not into a single value. Most of the aggregation functions theory does not apply directly. In our contribution, we present an attempt to start building a theoretical background of complex aggregation. We introduce and discuss exactly mergeable summaries for which it holds for merging of disjoint sets of units \[ Σ(A \cup B) = F( Σ(A),Σ(B)),\qquad \mbox{ for } \quad A\cap B = \emptyset .\]

cs.LG↗

arXiv2019

Corrected overlap weight and clustering coefficient

We discuss two well known network measures: the overlap weight of an edge and the clustering coefficient of a node. For both of them it turns out that they are not very useful for data analytic task to identify important elements (nodes or links) of a given network. The reason for this is that they attain their largest values on maximal subgraphs of relatively small size that are more probable to appear in a network than that of larger size. We show how the definitions of these measures can be corrected in such a way that they give the expected results. We illustrate the proposed corrected measures by applying them on the US Airports network using the program Pajek.

cs.SI↗

arXiv2019

Temporal Bibliographic Networks

We present two ways (instantaneous and cumulative) to transform bibliographic networks, using the works' publication year, into corresponding temporal networks based on temporal quantities. We also show how to use the addition of temporal quantities to define interesting temporal properties of nodes, links and their groups thus providing an insight into evolution of bibliographic networks. Using the multiplication of temporal networks we obtain different derived temporal networks providing us with new views on studied networks. The proposed approach is illustrated with examples from the collection of bibliographic networks on peer review.

cs.SI↗

arXiv2019

On Fractional Approach to Analysis of Linked Networks

In this paper, we present the outer product decomposition of a product of compatible linked networks. It provides a foundation for the fractional approach in network analysis. We discuss the standard and Newman's normalization of networks. We propose some alternatives for fractional bibliographic coupling measures.

cs.SI↗

arXiv2018

Social Network Analysis: Bibliographic Network Analysis of the Field and its Evolution / Part 1. Basic Statistics and Citation Network Analysis

In this paper, we present the results of the study on the development of social network analysis (SNA) discipline and its evolution over time, using the analysis of bibliographic networks. The dataset consists of articles from the Web of Science Clarivate Analytics database and those published in the main journals in the field (70,000+ publications), created by searching for the key word "social network*." From the collected data, we constructed several networks (citation and two-mode, linking publications with authors, keywords and journals). Analyzing the obtained networks, we evaluated the trends in the field`s growth, noted the most cited works, created a list of authors and journals with the largest amount of works, and extracted the most often used keywords in the SNA field. Next, using the Search path count approach, we extracted the main path, key-route paths and link islands in the citation network. Based on the probabilistic flow node values, we identified the most important articles. Our results show that authors from the social sciences, who were most active through the whole history of the field development, experienced the "invasion" of physicists from 2000's. However, starting from the 2010's, a new very active group of animal social network analysis has emerged.

physics.soc-ph↗

arXiv2016

Semirings for temporal network analysis

In the article, we describe a new algebraic approach to the temporal network analysis based on the notion of temporal quantities. We define the semiring for computing the foremost journey and the traveling semirings for the analysis of temporal networks where the latency is given, the waiting times are arbitrary, and some other information on the links are known. We use the operations in the traveling semiring to compute a generalized temporal betweenness centrality of the nodes that corresponds to the importance of the nodes with respect to the ubiquitous foremost journeys in a temporal network.

cs.SI↗

arXiv2015

An algebraic approach to temporal network analysis based on temporal quantities

In a temporal network, the presence and activity of nodes and links can change through time. To describe temporal networks we introduce the notion of temporal quantities. We define the addition and multiplication of temporal quantities in a way that can be used for the definition of addition and multiplication of temporal networks. The corresponding algebraic structures are semirings. The usual approach to (data) analysis of temporal networks is to transform it into a sequence of time slices -- static networks corresponding to selected time intervals and analyze each of them using standard methods to produce a sequence of results. The approach proposed in this paper enables us to compute these results directly. We developed fast algorithms for the proposed operations. They are available as an open source Python library TQ (Temporal Quantities) and a program Ianus. The proposed approach enables us to treat as temporal quantities also other network characteristics such as degrees, connectivity components, centrality measures, Pathfinder skeleton, etc. To illustrate the developed tools we present some results from the analysis of Franzosi's violence network and Corman's Reuters terror news network.

cs.SI↗

arXiv2015

Clustering of Modal Valued Symbolic Data

Symbolic Data Analysis is based on special descriptions of data - symbolic objects (SO). Such descriptions preserve more detailed information about units and their clusters than the usual representations with mean values. A special kind of symbolic object is a representation with frequency or probability distributions (modal values). This representation enables us to consider in the clustering process the variables of all measurement types at the same time. In the paper a clustering criterion function for SOs is proposed such that the representative of each cluster is again composed of distributions of variables' values over the cluster. The corresponding leaders clustering method is based on this result. It is also shown that for the corresponding agglomerative hierarchical method a generalized Ward's formula holds. Both methods are compatible - they are solving the same clustering optimization problem. The leaders method efficiently solves clustering problems with large number of units; while the agglomerative method can be applied alone on the smaller data set, or it could be applied on leaders, obtained with compatible nonhierarchical clustering method. Such a combination of two compatible methods enables us to decide upon the right number of clusters on the basis of the corresponding dendrogram. The proposed methods were applied on different data sets. In the paper, some results of clustering of ESS data are presented.

stat.ML↗

arXiv2015

Generalized Two-mode Cores

The node set of a two-mode network consists of two disjoint subsets and all its links are linking these two subsets. The links can be weighted. We developed a new method for identifying important sub-networks in two-mode networks. The method combines and extends the ideas from generalized cores in one-mode networks and from (p, q)- cores for two-mode networks. In this paper we introduce the notion of generalized two-mode cores and discuss some of their properties. An efficient algorithm to determine generalized two-mode cores and an analysis of its complexity are also presented. For illustration some results obtained in analyses of real-life data are presented.

cs.SI↗

arXiv2014

Network analysis of Zentralblatt MATH data

We analyze the data about works (papers, books) from the time period 1990-2010 that are collected in Zentralblatt MATH database. The data were converted into four 2-mode networks (works $\times$ authors, works $\times$ journals, works $\times$ keywords and works $\times$ MSCs) and into a partition of works by publication year. The networks were analyzed using Pajek -- a program for analysis and visualization of large networks. We explore the distributions of some properties of works and the collaborations among mathematicians. We also take a closer look at the characteristics of the field of graph theory as were realized with the publications.

cs.SI↗

arXiv2013

On bibliographic networks

In the paper we show that the bibliographic data can be transformed into a collection of compatible networks. Using network multiplication different interesting derived networks can be obtained. In defining them an appropriate normalization should be considered. The proposed approach can be applied also to other collections of compatible networks. We also discuss the question when the multiplication of sparse networks preserves sparseness. The proposed approaches are illustrated with analyses of collection of networks on the topic "social network" obtained from the Web of Science.

cs.SI↗

arXiv2006

Probabilistic Inductive Classes of Graphs

Models of complex networks are generally defined as graph stochastic processes in which edges and vertices are added or deleted over time to simulate the evolution of networks. Here, we define a unifying framework - probabilistic inductive classes of graphs - for formalizing and studying evolution of complex networks. Our definition of probabilistic inductive class of graphs (PICG) extends the standard notion of inductive class of graphs (ICG) by imposing a probability space. A PICG is given by: (1) class B of initial graphs, the basis of PICG, (2) class R of generating rules, each with distinguished left element to which the rule is applied to obtain the right element, (3) probability distribution specifying how the initial graph is chosen from class B, (4) probability distribution specifying how the rules from class R are applied, and, finally, (5) probability distribution specifying how the left elements for every rule in class R are chosen. We point out that many of the existing models of growing networks can be cast as PICGs. We present how the well known model of growing networks - the preferential attachment model - can be studied as PICG. As an illustration we present results regarding the size, order, and degree sequence for PICG models of connected and 2-connected graphs.

math.DS↗